// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include "solverbase.h"
#include <Eigen/QR>

template<typename MatrixType>
void
qr(const MatrixType& m)
{
	Index rows = m.rows();
	Index cols = m.cols();

	typedef typename MatrixType::Scalar Scalar;
	typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;

	MatrixType a = MatrixType::Random(rows, cols);
	HouseholderQR<MatrixType> qrOfA(a);

	MatrixQType q = qrOfA.householderQ();
	VERIFY_IS_UNITARY(q);

	MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
	VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
}

template<typename MatrixType, int Cols2>
void
qr_fixedsize()
{
	enum
	{
		Rows = MatrixType::RowsAtCompileTime,
		Cols = MatrixType::ColsAtCompileTime
	};
	typedef typename MatrixType::Scalar Scalar;
	Matrix<Scalar, Rows, Cols> m1 = Matrix<Scalar, Rows, Cols>::Random();
	HouseholderQR<Matrix<Scalar, Rows, Cols>> qr(m1);

	Matrix<Scalar, Rows, Cols> r = qr.matrixQR();
	// FIXME need better way to construct trapezoid
	for (int i = 0; i < Rows; i++)
		for (int j = 0; j < Cols; j++)
			if (i > j)
				r(i, j) = Scalar(0);

	VERIFY_IS_APPROX(m1, qr.householderQ() * r);

	check_solverbase<Matrix<Scalar, Cols, Cols2>, Matrix<Scalar, Rows, Cols2>>(m1, qr, Rows, Cols, Cols2);
}

template<typename MatrixType>
void
qr_invertible()
{
	using std::abs;
	using std::log;
	using std::max;
	using std::pow;
	typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
	typedef typename MatrixType::Scalar Scalar;

	STATIC_CHECK((internal::is_same<typename HouseholderQR<MatrixType>::StorageIndex, int>::value));

	int size = internal::random<int>(10, 50);

	MatrixType m1(size, size), m2(size, size), m3(size, size);
	m1 = MatrixType::Random(size, size);

	if (internal::is_same<RealScalar, float>::value) {
		// let's build a matrix more stable to inverse
		MatrixType a = MatrixType::Random(size, size * 4);
		m1 += a * a.adjoint();
	}

	HouseholderQR<MatrixType> qr(m1);

	check_solverbase<MatrixType, MatrixType>(m1, qr, size, size, size);

	// now construct a matrix with prescribed determinant
	m1.setZero();
	for (int i = 0; i < size; i++)
		m1(i, i) = internal::random<Scalar>();
	RealScalar absdet = abs(m1.diagonal().prod());
	m3 = qr.householderQ(); // get a unitary
	m1 = m3 * m1 * m3;
	qr.compute(m1);
	VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
	// This test is tricky if the determinant becomes too small.
	// Since we generate random numbers with magnitude range [0,1], the average determinant is 0.5^size
	VERIFY_IS_MUCH_SMALLER_THAN(
		abs(absdet - qr.absDeterminant()),
		numext::maxi(RealScalar(pow(0.5, size)), numext::maxi<RealScalar>(abs(absdet), abs(qr.absDeterminant()))));
}

template<typename MatrixType>
void
qr_verify_assert()
{
	MatrixType tmp;

	HouseholderQR<MatrixType> qr;
	VERIFY_RAISES_ASSERT(qr.matrixQR())
	VERIFY_RAISES_ASSERT(qr.solve(tmp))
	VERIFY_RAISES_ASSERT(qr.transpose().solve(tmp))
	VERIFY_RAISES_ASSERT(qr.adjoint().solve(tmp))
	VERIFY_RAISES_ASSERT(qr.householderQ())
	VERIFY_RAISES_ASSERT(qr.absDeterminant())
	VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}

EIGEN_DECLARE_TEST(qr)
{
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(
			qr(MatrixXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_2(qr(MatrixXcd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2),
									internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2))));
		CALL_SUBTEST_3((qr_fixedsize<Matrix<float, 3, 4>, 2>()));
		CALL_SUBTEST_4((qr_fixedsize<Matrix<double, 6, 2>, 4>()));
		CALL_SUBTEST_5((qr_fixedsize<Matrix<double, 2, 5>, 7>()));
		CALL_SUBTEST_11(qr(Matrix<float, 1, 1>()));
	}

	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(qr_invertible<MatrixXf>());
		CALL_SUBTEST_6(qr_invertible<MatrixXd>());
		CALL_SUBTEST_7(qr_invertible<MatrixXcf>());
		CALL_SUBTEST_8(qr_invertible<MatrixXcd>());
	}

	CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
	CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
	CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
	CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
	CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
	CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());

	// Test problem size constructors
	CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
}
